Probing the presence of planets in transition discs' cavities via warps: the case of TW Hya

We are entering the era in which observations of protoplanetary discs properties can indirectly probe the presence of massive planets or low mass stellar companions interacting with the disc. In particular, the detection of warped discs can provide important clues to the properties of the star-disc system. In this paper we show how observations of warped discs can be used to infer the dynamical properties of the systems. We concentrate on circumbinary discs, where the mass of the secondary can be planetary. First, we provide some simple relations that link the amplitude of the warp in the linear regime to the parameters of the system. Secondly, we apply our method to the case of TW Hya, a transition disc for which a warp has been proposed based on spectroscopic observations. Assuming values for the disc and stellar parameters from observations, we conclude that, in order for a warp induced by a planetary companion to be detectable, the planet mass should be large ($M_{\rm p} \approx 10 - 14M_{\rm J}$) and the disc should be viscous ($\alpha \approx 0.15 - 0.25$). We also apply our model to LkCa 15 and T Cha, where a substellar companion has been detected within the central cavity of the transition discs.Comment: 12 pages, 4 figures, 2 tables. Accepted for publication in MNRA

On Modal μ -Calculus and Gödel-Löb Logic

We show that the modal μ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modalμ ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formul

The modal μ-calculus hierarchy over restricted classes of transition systems

We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternation-free fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite model

An efficient Bouc & Wen approach for seismic analysis of masonry tower

The assessment of existing masonry towers under exceptional loads, such as earthquake loads, requires reliable, expedite and efficient methods of analysis. These approaches should take into account both the randomness that affects the masonry properties (in some cases also the distribution of the elastic parameters) and, of course, the nonlinear behavior of masonry. Considering the need of simplified but effective methods to assess the seismic response of such structures, the paper proposes an efficient approach for seismic assessment of masonry towers assuming the material properties as a stochastic field. As a prototype of masonry towers a cantilever beam is analyzed assuming that the first modal shape governs the structural motion. With this hypothesis a nonlinear hysteretic Bouc & Wen model is employed to reproduce the system response which is subsequently employed to evaluate the response bounds. The results of the simplified approach are compared with the results of a finite element model to show the effectiveness of the method

A Hybrid Approach for the Random Dynamics of Uncertain Systems under Stochastic Loading

This paper presents a hybrid Galerkin/perturbation approach based on Radial Basis Functions for the dynamic analysis of mechanical systems affected by randomness both in their parameters and loads. In specialized literature various procedures are nowadays available to evaluate the response statistics of such systems, but sometimes a choice has to be made between simpler methods (that could provide unreliable solutions) and more complex methods (where accurate solutions are provided by means of a heavy computational effort). The proposed method combines a Radial Basis Functions (RBF) based Galerkin method with a perturbation approach for the approximation of the system response. In order to keep the number of differential equations to be solved as low as possible, a Karhunen-Loève (KL) expansion for the excitation is used. As case study a non-linear single degree of freedom (SDOF) system with random parameters subjected to a stochastic windtype load is analyzed and discussed in detail; obtained numerical solutions are compared with the results given by Monte Carlo Simulation (MCS) to provide a validation of the proposed approach. The proposed method could be a valid alternative to the classical procedures as it is able to provide satisfactory approximations of the system response

Traffic-induced vibrations on a simple frame: Influence of external action coherence on structural response

The study of the traffic-induced response of a simple frame structure is presented. In particular, the effect of the spatial correlation, among the traffic-induced ground displacements, is discussed by means of a parametric study to achieve the purpose of outlining those configurations yielding the less-conservative structural response. Ground excitations are estimated by the model of Hunt (J. Sound Vib. 1991; 1:41–51; J. Sound Vib. 1991; 1:53–70) assuming a quarter-car vehicle model moving on an uneven roadway placed on the top of a homogeneous half-space. The structure consists of a rigid slab supported by four columns and subjected by traffic-induced forces suitably condensed in its center of mass. Copyright © 2008 John Wiley & Sons, Ltd